Mendeley出力
＜図書＞
Digital nets and sequences : discrepancy theory and quasi-Monte Carlo integration
| 責任表示 | Josef Dick, Friedrich Pillichshammer |
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| データ種別 | 図書 |
| 出版情報 | Cambridge : Cambridge University Press , 2010 |
| 本文言語 | 英語 |
| 大きさ | xvii, 600 p. ; 26 cm |
| 概要 | "This book is a comprehensive treatment of contemporary quasi-Monte Carlo methods, digital nets and sequences, and discrepancy theory which starts from scratch with detailed explanations of the basic ...oncepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi-Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses with numerous examples, exercises and llustrations"--続きを見る |
| 目次 | Machine generated contents note: Preface; Notation; 1. Introduction; 2. Quasi-Monte Carlo integration, discrepancy and reproducing kernel Hilbert spaces; 3. Geometric discrepancy; 4. Nets and sequences; 5. Discrepancy estimates and average type results; 6. Connections to other discrete objects; 7. Duality Theory; 8. Special constructions of digital nets and sequences; 9. Propagation rules for digital nets; 10. Polynomial lattice point sets; 11. Cyclic digital nets and hyperplane nets; 12. Multivariate integration in weighted Sobolev spaces; 13. Randomisation of digital nets; 14. The decay of the Walsh coefficients of smooth functions; 15. Arbitrarily high order of convergence of the worst-case error; 16. Explicit constructions of point sets with best possible order of L2-discrepancy; Appendix A. Walsh functions; Appendix B. Algebraic function fields; References; Index. |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
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: hbk | 理系図3F 数理独自 | DICK/3/1 | 2010 |
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033212010003810 |
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書誌詳細
| 一般注記 | Includes bibliographical references and index |
|---|---|
| 著者標目 | Dick, Josef Pillichshammer, Friedrich |
| 書誌ID | 1001432937 |
| ISBN | 9780521191593 |
| NCID | BB03602827 |
| 巻冊次 | : hbk ; ISBN:9780521191593 |
| 登録日 | 2010.11.02 |
| 更新日 | 2010.11.02 |